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The Helgason Fourier transform for homogeneous vector bundles over compact Riemannian symmetric spaces – the local theory. (English) Zbl 1060.43004
From the author’s summary: The Helgason Fourier transform on noncompact Riemannian symmetric spaces \(G/K\) is generalized to the homogeneous vector bundles over the compact dual spaces \(U/K.\) The scalar theory on \(U/K\) was considered by Sherman (the local theory for \(U/K\) of arbitrary rank, and the global theory for \(U/K\) of rank one). In this paper we extend the local theory of Sherman to arbitrary homogeneous vector bundles on \(U/K.\) For \(U/K\) of rank one we also obtain a generalization of the Cartan-Helgason theorem valid for any \(K\)-type.

MSC:
43A85 Harmonic analysis on homogeneous spaces
42C15 General harmonic expansions, frames
22E46 Semisimple Lie groups and their representations
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